the graph shows $g(x)$, which is a transformation of $f(x)=|x|$. write the function rule for $g(x)$. \nwrite…

the graph shows $g(x)$, which is a transformation of $f(x)=|x|$. write the function rule for $g(x)$. \nwrite your answer in the form $a|x - h|+k$, where $a$, $h$, and $k$ are integers or simplified fractions. \n$g(x)=$

the graph shows $g(x)$, which is a transformation of $f(x)=|x|$. write the function rule for $g(x)$. \nwrite your answer in the form $a|x - h|+k$, where $a$, $h$, and $k$ are integers or simplified fractions. \n$g(x)=$

Answer

Answer:

( g(x)=\frac{1}{4}|x| )

Explanation:

Step1: Recall the transformation formula

The general form of a transformation of ( f(x) = |x| ) is ( g(x)=a|x - h|+k ). Here, ( h = 0,k = 0 ) (since the vertex of ( g(x) ) is at the origin ((0,0)) as in ( f(x)=|x|)).

Step2: Find the value of ( a )

Take a point on ( g(x) ). For example, when ( x = 4 ), ( y = 1 ). Substitute ( x = 4,y = 1,h = 0,k = 0 ) into ( g(x)=a|x - h|+k ). We get ( 1=a|4 - 0|+0 ), i.e., ( 1 = 4a ). Solving for ( a ), we have ( a=\frac{1}{4} ).

So the function rule for ( g(x) ) is ( g(x)=\frac{1}{4}|x| ).